The Correct Answer and Explanation is:
Of course. Here is the correct answer and a detailed explanation.
Answer: 23 1/3 %
Explanation
The problem requires us to calculate the value of the expression (14/15 – 14/20) and then express that value as a percentage. This can be accomplished in two main steps: first, performing the subtraction of the fractions, and second, converting the result into a percentage.
Step 1: Subtracting the Fractions
The initial expression is a subtraction of two fractions: 14/15 and 14/20. To add or subtract fractions, they must have a common denominator. We need to find the least common multiple (LCM) of the two denominators, 15 and 20.
- Multiples of 15 are: 15, 30, 45, 60, 75, …
- Multiples of 20 are: 20, 40, 60, 80, …
The least common multiple of 15 and 20 is 60. This will be our least common denominator (LCD).
Now, we convert each fraction to an equivalent fraction with a denominator of 60.
For the fraction 14/15, we divide the LCD by the original denominator (60 ÷ 15 = 4) and multiply both the numerator and denominator by this result:
(14 × 4) / (15 × 4) = 56/60.
For the fraction 14/20, we do the same (60 ÷ 20 = 3):
(14 × 3) / (20 × 3) = 42/60.
With the fractions having a common denominator, we can now perform the subtraction:
56/60 – 42/60 = (56 – 42) / 60 = 14/60.
Before converting to a percentage, it is helpful to simplify the fraction 14/60. Both the numerator and the denominator are divisible by 2:
14 ÷ 2 = 7
60 ÷ 2 = 30
So, the simplified fraction is 7/30.
Step 2: Converting the Fraction to a Percentage
The final task is to express the fraction 7/30 as a percentage. The word “percent” literally means “out of one hundred”. To convert any fraction to a percentage, we multiply it by 100 and add the percent symbol (%).
Calculation:
(7/30) × 100% = (7 × 100) / 30 % = 700 / 30 %
We can simplify the fraction 700/30 by dividing both the numerator and the denominator by their greatest common divisor, which is 10:
700 ÷ 10 = 70
30 ÷ 10 = 3
This gives us 70/3 %.
To make this improper fraction easier to understand, we can convert it to a mixed number by dividing 70 by 3.
70 ÷ 3 = 23 with a remainder of 1.
Thus, 70/3 is equivalent to the mixed number 23 1/3.
Therefore, the final answer is 23 1/3 %.
